a tree casts a shadow of 34 feet. the angle of th elevation of the sun is 52. what is the height of the tree?
To find the height of the tree, we can use trigonometry and the concept of similar triangles. Here's how you can do it:
Step 1: Understand the problem
The information we have is that the tree casts a shadow of 34 feet and the angle of elevation of the sun is 52 degrees.
Step 2: Draw a diagram
Draw a diagram representing the situation. Label the height of the tree as "h" and the distance from the base of the tree to the tip of the shadow as "d". The angle of elevation (52 degrees) can be marked at the top.
/|
/ |
/ |
h / | d
/ |
/____|
(shadow)
Step 3: Identify the trigonometric relationship
The tangent function relates the angle of elevation (52 degrees), the height of the tree (h), and the distance to the shadow (d) as follows:
tan(52°) = h/d
Step 4: Solve for the height of the tree
Rearrange the equation to solve for "h":
h = d * tan(52°)
Step 5: Plug in the values and calculate the height
According to the problem, the shadow's length, "d," is given as 34 feet.
h = 34 * tan(52°)
Using a calculator, find the tangent of 52 degrees:
tan(52°) ≈ 1.2799
Now substitute this value back into the equation and calculate the height of the tree:
h ≈ 34 * 1.2799 ≈ 43.5186 feet
Therefore, the height of the tree is approximately 43.5186 feet.
90 -52 = 38
law of sines
sin38/34 = sin52/h
h = 34 sin52/sin38
h = 43.5
or
tan 52 = h/34
h = 43.5